Europium-induced engineering of the spin-dependent electronic properties of monolayer graphene (Gr) on Co(0001) is presented. An enhancement of the charge transfer into Gr via Eu doping and the existence of a spin-polarized Gr-Co hybrid state formed by positioning Eu on top or beneath the Gr monolayer, in both cases with a single-spin character, occurs. While in the former case, the low-dispersive parabolic Gr-Co hybrid band is observed close to Fermi energy, when Eu is intercalated, the π* band flattens.